In addition, the percolation threshold is quite different as \(W_c=3.0\)  and \(W_c=0.0\)  for the case of the interacting and non-interacting systems respectively.
It is worth mentioning, that beyond the error of our analysis, the percolation threshold for the case of the interacting system coincides with the ergodic to MBL transition point \(W_c\approx 3.5\)  [1]} which shows that our system experiences a percolation transition in its corresponding LIOMs across the MBL transition.
